 | Percey Franklyn Smith, Arthur Sullivan Gale - 1905 - 240 sider
...• ] ji j14. sin2x = 2 sinx cos x ; cos 2 ж = cos2x — sin2x ; tan2x = 16. Theorem. Law of sines. In any triangle the sides are proportional to the sines of the opposite angles; abc that is, - — r = ^-;; = ^-^sm A sin В sm С 17. Theorem. Law of cosines. In any triangle the... | |
 | International Correspondence Schools - 1906 - 634 sider
...naming the sides and angles of a triangle, see Plane Trigonometry, Part 1. 18. Principle of Sines. — In any triangle, the sides are proportional to the sines of the opposite angles. That is, a. _ sin A a _ sin A .b sin R b sin B1 c sin C' c sin C Let ABC, Fig. 6, be any triangle and... | |
 | 1906 - 230 sider
...the sides and angles of a triangle, see Plane Trigonometry, Part 1. 18. Principle of Sines. — fn any triangle, the sides are proportional to the sines of the opposite angles. That is, a _ sin A a _ sin A b, _ sin B b sin B^ c sin C' c sin C Let ABC, Fig. 6, be any triangle... | |
 | Charles Samuel Jackson, Robert Moir Milne - 1907 - 408 sider
...Lami's theorem is the translation into a statical proposition of the trigonometrical proposition that in any triangle the sides are proportional to the sines of the opposite angles. c Resolving. — If ABC is any A and AA', BB' and CC' are drawn perpendicular on any straight line... | |
 | A. P. W. Williamson - 1909 - 410 sider
...opposite one of them to find the other parts. EXAMPLE I.— Given В = 67° 22' 49", & = 45, с = 39. In any triangle the sides are proportional to the sines of the opposite angles, that is — c- • т > L- /^ Sin С с b : с :: Sin В : Sin С, or --:---- = ... ~ с. Sin В .... | |
 | William Charles Brenke - 1910 - 374 sider
...to obtain. Additional relations will then be derived from these. The Law of Sines. — In any plane triangle, the sides are proportional to the sines of the opposite angles. Let ABC be the triangle, CD one of its altitudes. Two cases arise, according as D falls within or without the... | |
 | Herbert E. Cobb - 1911 - 296 sider
...perpendicular from A to a we may obtain, in a similar manner, sin C sin B bc sin A sin B sin C LAW OF SINES. In any triangle the sides are proportional to the sines of the opposite angles. When a side and two angles of a triangle are given we may find the other two sides by this law. PROBLEMS... | |
 | Ernest William Hobson - 1911 - 432 sider
...—a cos В + b cos A ) a/sin A = 6/sin В = c/sin С (2). The equations (2) express the fact that, in any triangle, the sides are proportional to the sines of the opposite angles. 120. The relations (2) may also be proved thus : — Draw the circle circumscribing the triangle ABC,... | |
 | Robert Édouard Moritz - 1913 - 562 sider
...sin С. (г) Equation (i) or (2) embodies what is known as the Law of Sines, which states that, — In any triangle the sides are proportional to the sines of the opposite angles. (b) Second proof. The Law of Sines may be proven in another way, which at the same time brings out... | |
 | Earle Bertram Norris, Kenneth Gardner Smith, Ralph Thurman Craigo - 1913 - 234 sider
...written in the following form : abc sin A - sin B- sin C Written in words this would be as follows: "In any triangle, the sides are proportional to the sines of the angles opposite them." 139. Application of Laws to Problems. — There may be four possible cases of... | |
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In any triangle, the sides are proportional to the sines of the opposite angles. That is, sin A = sin B... 
